A first-order reaction A ⟶B has the rate constant k=3.2 ×10^-3 s^-1 . If the initial concentrati

step 1 To calculate the rate of a first -order reaction, we need to know the first -order rate law, whi

A first-order reaction A ⟶B has the rate constant k=3.2...

A first-order reaction $\mathrm{A} \longrightarrow \mathrm{B}$ has the rate constant $k=3.2 \times 10^{-3} \mathrm{s}^{-1} .$ If the initial concentration of $\mathrm{A}$ is $2.5 \times 10^{-2} \mathrm{M},$ what is the rate of the reaction at $t=660 \mathrm{s} ?$

Key Concepts

First-Order Reaction Kinetics

This concept describes reactions in which the rate of reaction is directly proportional to the concentration of one reactant. In mathematical terms, the rate law is expressed as rate = k[A], where k is the rate constant. The behavior of these reactions is often analyzed using exponential decay functions over time.

Exponential Decay

Exponential decay refers to the process by which the concentration of a reactant decreases over time in a first-order reaction. The concentration at any time t can be calculated using the equation [A] = [A]? exp(?kt), capturing the characteristic decrease of the reactant over time.

Rate Constant

The rate constant (k) in reaction kinetics is a proportionality factor that quantifies the speed of a reaction for a given set of conditions. In first-order reactions, it has units of inverse time (such as s?¹) and directly influences the rate at which the reactant concentration decays.

Reaction Rate

Reaction rate is the measure of how quickly the concentration of reactants changes over time. For first-order reactions, the rate at a given time can be determined by multiplying the rate constant by the current concentration of the reactant, reflecting how the instantaneous rate depends on the amount of reactant remaining.

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